V. Derenchuk

Effects of rf voltage modulation on particle motion

Abstract The effects of rf voltage modulation on synchrotron motion were studied experimentally. The experimental data revealed the resonance islands generated by the rf voltage modulation. With electron cooling, beam particles were observed to damp to the basins of these resonance islands or attractors, which were observed to rotate about the origin of the phase space at a half of the modulation frequency. The measured amplitude of the attractors as a function of the modulation frequency agreed very well with the theoretical prediction. The Poincare maps in the resonance rotating frame were obtained from the experimental data and compared with tori of the Hamiltonian flow. Based on our theoretical formulation, slow beam extraction using rf voltage modulation and a bent crystal are also studied.

Space charge effects and intensity limits of electron-cooled bunched beams

For stripping injection of proton beams in the IUCF Cooler, electron cooling permits us to accumulate beam currents several times higher than what can be obtained without cooling. Paradoxically, the electron cooling system also appears to be responsible for limiting peak currents in the ring at 45 MeV to about 6 mA. Thus the tool which allows us to accumulate beam also prevents us from accumulating more beam. At this point we can account for some of the observed beam features when we include space charge effects. Presently, we do not, however, have any techniques to counteract the space charge effects and thus raise this intensity limit.

Measurement of space charge effect on transverse emittance

The SNS accumulator ring is designed to compress 1.5/spl times/10/sup 14/ 1 GeV protons from a bunch train of 1000 /spl mu/s H/sup -/ to a single proton bunch with bunch length 700 ns. The injection scenario of the SNS is experimentally simulated at the Cooler Injector Synchrotron (CIS) at Indiana University. A 100 /spl mu/s, 7 MeV H/sup -/ bunch train from the RFQ and DTL is compressed into a single proton bunch with bunch length /spl les/ 150 ns. The transverse rms emittance of the 7 MeV beam is measured by the quadrupole tuning method in the CIS extraction line. Measurements are taken at various beam intensities with peak currents ranging from a few mA to hundreds of mA. Results are compared with simulation, and the effects of multiple strip foil transits and space charge are discussed.

Determination of the linear coupling resonance strength using 2D invariant Tori

Experimentally obtained Poincare maps in the resonant precessing frame for particle motion with linear coupling revealed invariant tori of the 2D Hamiltonian. Using these tori, we obtained the linear coupling strength, the tune shift with betatron amplitude coefficient and the proximity parameter to the resonance. The coupling strengh obtained with this method agreed well with that obtained from measuring the betatron tune separation of the normal modes.

Longitudinal phase‐space measurements at IUCF

Synchrotron motion in the IUCF cooler ring was studied using turn‐by‐turn beam tracking on ten‐turn intervals, where the beam phase relative to the rf and the closed‐orbit position in a high‐dispersion region were measured. The synchrotron tune shift with amplitude was measured and is compared with theory. The driven response of the system was also studied using the same techniques, and was found to share many of the same characteristics of other parametric resonant systems. The experimental results did not exhibit any effects of bunch decoherence expected from the tune shift with amplitude.

Betatron coupling correction at the IUCF cooler, leading to improved determination of fourth‐order resonance Hamiltonian

Recently the Hamiltonian of particle motion near a resonance condition was deduced at the Indiana University Cyclotron Facility Cooler Ring. It was found that linear betatron coupling complicated the analysis. A coupling correction scheme is described which reduced the coupling coefficient from 0.03 to 0.0012. When particles were kicked onto resonance islands with the coupling reduced, the island motion was stable for upwards of 1×106 turns. This stable island motion allowed for the determination of higher‐order terms in the Hamiltonian.

Modeling of the IUCF cooler synchrotron

Measurements of lattice parameters for the Indiana University Cyclotron Facility (IUCF) Cooler synchrotron at betatron tunes close to a sum resonance line are discussed. The measured beta functions at 36 quadrupole locations and the dispersion functions at 35 Beam Position Monitor (BPM) locations are compared with calculations. The methods used to make the above measurements and the data analysis are described.

Beam motions near separatrix

Experimental data on particle motion near the separatrix of the one dimensional (1-D) fourth-integer islands are analyzed. When the beam bunch is initially kicked to the separatrix orbit, we observed a strong decoherence in the coherent betatron motion. We find that, through intensive particle tracking simulation analysis, the decoherence has resulted from the beam being split into beamlets in the betatron phase space. However, we also observe an unexpected recoherence of coherence signal, which may result form a modulated closed orbit or the homoclinic structure near the separatrix.